Thanks for the pm - I've checked the issue.
It seems that your httpd server / host firewall is configured to allow only some "User-Agent" values. When I was connecting with Firefox, the .../index.php?action=admin URL displayed properly (login page was there).
However, when Java SMF Backup wanted to connect to the same URL, your host replied directly with 403 auth denied.
After some trial and error, I found the difference. Java SMF Backup uses Apache Jakarta Http Client which, by default, has User-Agent header with value "Jakarta Commons-HttpClient/3.1".
Only after I made the application to fake the User-Agent by replacing it with Firefox one: "Mozilla/5.0 (Windows; U; Windows NT 6.1; en-US; rv:1.9.1.5) Gecko/20091102 Firefox/3.5.5 (.NET CLR 3.5.30729)" only then the application was able to connect and do proper backup.
Do you have control over that httpd server / reverse proxy / etc, which replies 403 when it doesn't recognize an "User-Agent" ? To me it seems a way to weed out robots. If so, please add the user agent above (Jakarta....) to the allowed list of user agents.
Thanks,